题目描述

Appropriate temperature changes are essential for brewing delicious tea. Noli has been taught a recipe for delicious tea.

The recipe is represented by a sequence of non-negative integers $A = a_0, a_1, a_2, \ldots, a_N, a_{N+1}$ of length $N+2$. She must change the temperature accordingly.

Raising the temperature is hard work. The cost of a recipe $A$ is defined by the following $f(A)$.

$$f(A) = \sum_{i=0}^{N} \max(0, a_{i+1} - a_i)$$

Noli has forgotten the recipe she was taught. All she remembers is that $a_0 = a_{N+1} = 0$ and that the cost was $K$.

How many possible recipes can be considered? Find the remainder of the number of possible recipes divided by $998244353$.

Note that two recipes are different when the values of $a_i$ are different for any $i (0 \leq i \leq N+1)$.

输入格式

$N \ K$

The input satisfies the following constraints.

• All inputs consist of integers.
• $1 \leq N \leq 2 \times 10^5$
• $0 \leq K \leq 2 \times 10^5$

输出格式

Output the remainder of the number of possible recipes divided by $998244353$. Add a new line at the end of the output.

2 2

5

100 0 

1

300 300

527212271

200000 200000

885086300

提示

In Sample Input 1, There are five possible sequences $A$.

• $\{0,2,0,0\}$
• $\{0,0,2,0\}$
• $\{0,1,2,0\}$
• $\{0,2,1,0\}$
• $\{0,2,2,0\}$